$\begingroup$stats::predict is a generic function, it doesn't do any actual prediction by itself. You pass it a model object and it will compute the prediction for that model. If you pass in a time series model it will "consider the year". This isn't so much a question about R, you just need to find a good model for this situation (many related, very short time series) which will allow you to share information about the dynamics across series.$\endgroup$
– Chris HaugFeb 27 '17 at 15:03